Cohomologie De Hochschild Des Surfaces De Klein
| dc.creator | Butin, Frédéric | |
| dc.date | 2008-03-23 | |
| dc.date | 2008-04-28 | |
| dc.date.accessioned | 2026-07-07T12:17:51Z | |
| dc.date.available | 2026-07-07T12:17:51Z | |
| dc.description | Given a mechanical system $(M, \mathcal{F}(M))$, where $M$ is a Poisson manifold and $\mathcal{F}(M)$ the algebra of regular functions on $M$, it is important to be able to quantize it, in order to obtain more precise results than through classical mechanics. An available method is the deformation quantization, which consists in constructing a star-product on the algebra of formal power series $\mathcal{F}(M)[[\hbar]]$. A first step toward study of star-products is the calculation of Hochschild cohomology of $\mathcal{F}(M)$. The aim of this article is to determine this Hochschild cohomology in the case of singular curves of the plane -- so we rediscover, by a different way, a result proved by Fronsdal and make it more precise -- and in the case of Klein surfaces. The use of a complex suggested by Kontsevich and the help of Gröbner bases allow us to solve the problem. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/0803.3347 | |
| dc.identifier | http://arxiv.org/abs/0803.3347 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212214 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Commutative Algebra | |
| dc.subject | Quantum Algebra | |
| dc.subject | Rings and Algebras | |
| dc.title | Cohomologie De Hochschild Des Surfaces De Klein | |
| dc.type | text |